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중등수학
2010.10.29 21:29

원과 각의 이등분선

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문제 레벨 중등수학

원에 내접하는 삼각형ABC에서 변AB=6, 변AC=4, 각BOC=120도이고, 각 BAC의 이등분선과 변BC의 교점을 D라고 할때,

 

변AD의 길이는?

 

그림 첨부했어요, 풀어주세요 ㅠㅠ1.jpg




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  • ?
    수학사랑연구소 2010.11.03 00:09

    그림 파일을 변환하여 본문에 추가하였습니다.  그림을 보니까 문제가 무슨뜻인지 바로 보입니다.

    각 OBC= 각 OCB=30도 (이등변삼각형) 이네요.

    각 BAC =60도이므로 각 CAD=30도입니다.  

    길이를 이용한 정보가 필요할 것 같은데... ^^???

  • ?
    지민 2010.11.04 15:01

    풀었네요! 혹시 궁금하신 분들 계실까봐, 답 올립니다.

    삼각비 이용해서 푸는 문제에요.

     

    삼각형ABC의 넓이는 삼각형ABD와 삼각형ACD의 합으로 이루어져 있으므로

    삼각형ABC=(1/2)*6*4*sin60=(1/2)*6*(변AD)*sin30 + (1/2)*4*(변AD)*sin30 가 되어 변AD의 계산이 가능해집니다.

     

    본의아니게 제가 문제 올리고 제가

  • ?
    와니 2011.01.19 11:05

    중등 수학에서 sin에 대한 정확한 정의가 제대로 먹혀들어가지 않기 때문에

    음...;; 조금 난이도 있게이면 모를까 보통은 둘레정보(길이)를 약간은 주지 않을까요?

     

    중3이냐 중2냐에 따라서 좀 차이가 있을 듯요^^

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